For Richard Dawkins the ideal of education is to teach children how to think rather than what to think (The God Delusion, p. 327). Nevertheless, it is to be expected that the examples he gives of child abuse in education is the teaching of what Dawkins believes to be objective errors (The God Delusion, chapter 9). If what is taught is error, then the ‘how to think’ implicit in the lesson must also be erroneous. Who could disagree with Dawkins on the importance of teaching children the truth and how to think to discover the truth?

This essay examines Dawkins’ teaching of Darwinian evolution to the general public in The God Delusion and specifically to children in Dawkins’ Christmas lecture of 1991, “Climbing Mount Improbable”, minute 4:25.

Child Abuse (Teaching children error) by Dawkins, Caught on Camera

Whereas Darwinian evolution is mathematically coherent, Richard Dawkins’ understanding of it and his teaching of it are mathematically incoherent and erroneous. Even though he believes it, Dawkins’ version is still falsehood and incoherent thinking. To teach children falsehood and how to think incoherently is child abuse by Dawkins’ definition of child abuse. That abuse has been captured on video in the reference above.

Darwinian Evolution vs. Dawkins’ Version of it

In the video, Dawkins is right in identifying Darwinian evolution as a series of stages consisting of mutation and of natural, non-random selection. However, in Darwinian evolution mutation is explicitly random mutation. Dawkins makes two main errors. He substitutes non-random mutation for random mutation. Further, he mistakes an increase in the efficiency of mutation for an increase in the probability of success of natural selection.

Apparently due to a weak education in mathematics, Dawkins can’t see the distinction between random and non-random. He can’t see the distinction between efficiency and probability. Consequently, Dawkins teaches the error that the probability of success of evolution is increased by replacing a single Darwinian stage of random mutation and natural selection with a series of sub-stages.

In The God Delusion (p 121) he calls this replacement ‘breaking an improbability up into smaller pieces of improbability’. In the Christmas lecture, “Climbing Mount Improbable”, he calls it ‘smearing out the luck’. Such replacement does not affect the probability or, synonymously, the luck, in Darwinian evolution. It increases the efficiency of mutation.

Dawkins’ Numerical Illustration

In the Christmas lecture Dawkins proposes a numerical illustration, which is a perfect exemplar of Darwinian evolution involving three mutation sites of six mutations each. A three-dial lock of six positions each, such as a bicycle lock, is replaced by three one-dial locks, each of six positions.

Dawkins thinks that the probability of success in Darwinian evolution is determined by the number of different mutations defined in a stage of evolution. The three-dial lock defines 216 different mutations, 6 x 6 x 6. In contrast, the set of three one-dial locks defines a total of 18 different mutations, 6 + 6 + 6.

Dawkins claims that opening the three-dial lock requires a maximum of 216 ‘tries’ or a luck of 1/216, whereas the maximum number of ‘tries’ required to open the set of three one-dial locks is 18. Implicitly this is a luck of 1/18 in three increments of luck, each equaling 1/6. According to Dawkins, instead of having to get the luck in ‘one ridiculously large dollop’ of 1/216, the luck can be gotten in ‘dribs and drabs’ of 1/6. The luck has been ‘smeared out’.

Critique

It would take a maximum of 216 tries or mutations to open the three-dial lock and a maximum of 18 tries or mutations to open the set of three one-dial locks, just as Dawkins says. However, this is true only if the mutations are non-random. The probability of opening the locks in each of the two cases is 100% in Dawkins’ illustration of non-random mutation.

Because he thinks he is illustrating random mutation, Dawkins is oblivious to the fact that there is no difference in probability in the two cases. It is 100% in both. The contrast is 100% for the three-dial lock vs. 100% = 100% x 100% x 100% for the three one-dial locks.

Dawkins doesn’t know what determines the probability of success in Darwinian evolution. He mistakenly thinks it is the probability of a single random mutation, which would be 1/216 for the three-dial lock and 1/6 for each of the one-dial locks.

Dawkins is objectively abusing the children who comprise his audience by teaching error in the thought process and in the conclusion. In Dawkins’ illustration of non-random mutations the difference is not in luck. The luck, i.e. the probability of success, is 100% for both cases.

The difference is in the number of non-random mutations required for a success of 100%. The difference is that of 216 non-random mutations compared to 18 non-random mutations, which is an efficiency factor in non-random mutations of 216/18 = 12.

The two cases do not differ in luck, i.e. the probability of evolutionary success. They differ in the efficiency of mutation. What Dawkins taught the children is false in thought process and conclusion.

The Valid Mathematics of Darwinian Evolution

What does determine the probability of success of a single stage of random mutation and natural selection in Darwinian evolution? It is the total number of mutations randomly generated in that stage. Note that 216 non-random mutations will contain exactly one copy of the number which opens the three-dial lock.

What about 216 random mutations? The probability, P, of containing at least one copy of a specific number out of n numbers, where x numbers are generated at random to the base, n, is P = 1 – ((n – 1)/n)^x. In the lexicon of Darwinian evolution, P is the probability that the pool of a total of x random mutations contains at least one copy of the survivable mutation out of the n different mutations defined by the single stage of evolution.

When x = n = 216, P = 63.3%. If Dawkins’ 216 ‘tries’ were random, the probability of opening the three-dial lock would be 63.3%.

When x = n = 6, P = 66.5%. If Dawkins’ 6 ‘tries’ for each of the locks in the three lock set were random, the probability of opening each lock would be 66.5%. The net probability for the series of three one-dial locks, at a probability of 66.5% for each, is 29.4%, i.e. 66.5% x 66.5% x 66.5% = 29.4%.

In Dawkins’ lecture to the children, it would have been valid to compare 216 non-random mutations with the total of 18 non-random mutations for the series of three one-dial locks, if Dawkins had told the children the ‘tries’ were non-random and had nothing to do with luck or the probability of success of the algorithm. The success of the algorithm was 100% in both cases. Of course, Dawkins could not have told the children the truth that the ‘tries’ were non-random, because he obviously thought they were random. In thinking they were random, he thought they involved luck and taught that to the children.

If Dawkins understood the algorithm of Darwinian evolution, which he was attempting to teach the children, he should have chosen random mutation and a value of probability of evolutionary success, such as 90.9%, for both the three-dial lock and for the series of three one-dial locks.

If for each of the one-dial locks a pool of 19 random mutations is generated, the net probability of opening the three locks is 90.9%, i.e. 96.9% x 96.9% x 96.9%. If for the three-dial lock a pool of 517 random mutations is generated, the probability of opening the lock is 90.9%. In this example the probability of evolutionary success is the same, while the efficiency in random mutations is in favor of the set of three one-dial locks by a factor of 517/57 = 9.07.

Summary

It is not that the children could not understand efficiency. One process requires less input than another process to achieve the same goal. It is not that the children could not understand non-random mutation, e.g. placing a set of six dice face up such that the set displays each of the six different mutations of the face of a die. It is not that the children could not understand random mutation through an illustration such as the set of six faces resulting from rolling a set of six dice. It is that Dawkins doesn’t understand these concepts in the context of Darwinian evolution, even in his own illustration of three mutation sites of six mutations each. Consequently, he teaches children falsehood.

Replacing a single stage of random mutation and natural selection in Darwinian evolution by a series of sub-stages does not affect the probability of evolutionary success. It increases the efficiency of random mutation. Dawkins’ claim that such replacement breaks an improbability up into smaller pieces of improbability is not simply wrong. It is mathematically incoherent.

Dawkins is guilty of self-deception. He is also guilty of objective child abuse, by his definition of child abuse, when he teaches children that such gradualism in Darwinian evolution smears out the luck. It does not affect the luck. It increases the efficiency of mutation as his own example of non-random mutation illustrates.

A Ray of Hope

From the analytical tenor of his explanations of Darwinian evolution, it is apparent that Richard Dawkins is keenly interested in the mathematics of probability. This yields the hope that he might study the math, thereby leading to his realization of the errors he has been teaching as his solution to the ‘problem of improbability’ of Darwinian evolution in a one-off event and as the ‘problem of improbability’ of the existence of God.

It is evident from his explanations that Dawkins recognizes, however vaguely, the fact that Darwinian evolution is a mathematical algorithm involving mathematical probability. We are in debt to Richard Dawkins, among other evolutionary biologists, for his testimony that Darwinian evolution is a mathematical algorithm.

Nevertheless, Richard Dawkins is in debt to the thousands, whom he has convincingly taught his mathematically incoherent version of Darwinian evolution. He owes them the diligence not only to learn the basic mathematics involved, but publicly to correct the errors he has promulgated due to his lack of understanding of the Darwinian algorithm. Especially he owes it to the children, whom, by his definition, he has abused.

Bob Drury is retired. He has been fascinated with the reasonableness of the Faith since his junior year in high school in the mid-20th century for which the religion text was entitled, "Faith and Reason". That fascination has continued throughout his education in philosophy, math and science. In his essays he hopes to share that fascination with others. Read more at his website, They Have No Wine.

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